Geometric design tools for stiffness and vibration analysis of robotic mechanisms

Abstract

We present a methodology for the first-order stiffness and vibration analysis of general robotic systems including parallel mechanisms, based on geometric methods for kinematics and elasticity analysis. We exploit the uniformity and structure typically extant in parallel mechanisms to develop an accurate and computationally tractable method of stiffness and vibration analysis that is amenable 60 design iterations and optimization. By way of our analysis we formalize the notion of a mechanism's structural compliance matrix and derive an associated set of dynamic equations that model elastic effects without resorting to assumed modes or finite element models. Our methodology is illustrated with a case study involving the Eclipse, a novel six degree-of-freedom parallel mechanism designed for rapid machining.